Thank you all for your help.
I see that I have to split the lists in different segments to draw
them individually.
My dataset was a single-axis data, but it is trivial to add the X-Y
coordinates, so that's not a problem.
Finally I have adopted the solution proposed by Jean Marc, as it is
more efficient thant Dr Major Bob's solution (less Line calls) but
calling Graphics directly insted of ListPlot with the Axes option and
so on. It is faster than ListPlot.
Peter, I thought at first in drawing white lines, but white lines are
visible over dark lines when several graphs are plotted
simultaenously.
A good point in dividing the dataset in increasing small lists is that
now I can think in change the color of each segment depending on the
slope.
But the results are promising.
Thank you all!
Regards.